Unformatted text preview: with a mean of 50. If the variance of the r.v. is known to be 25, then what is a lower bound on the probability that this week’s production will be between 40 and 60? 4. Problem 81, page 182. 5. A voltage V is a function of time t and is given by V ( t ) = X cos(2 πft )+ Y sin(2 πft ) , in which f is the frequency (in Hz) and X and Y are two independent Gaussian zero mean r.v.’s of variance σ 2 . a. Show V ( t ) can be written as V ( t ) = R cos(2 πftΘ) . Hint: deﬁne R = ( X 2 + Y 2 ) . 5 . b Show R is a Rayleigh r.v. and Θ is uniformly distributed in [0 , 2 π ) , and these two r.v.’s are independent. 6. Problem 22, page 320. Hint: Use CLT and Gaussain r.v. to approximate the Binomial r.v....
View
Full Document
 Spring '08
 LORENZELLI
 Probability theory, Rayleigh, K. Yao, 16th Read pp, ﬁrst door

Click to edit the document details